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Programme of Course "Mathematical Economics and Finance"

Code:

DT0110

Type of course unit:

Bachelor Degree in Mathematics curriculum Generale: Elective
Master Degree in Mathematics curriculum Generale: Elective
Master Degree in Mathematical Engineering curriculum Comune: Elective

Level of course unit:

Undergraduate Degrees
Postgraduate Degrees

Semester:

1st semester

Number of credits:

Master Degree in Mathematics: 6 (workload 150 hours)
Master Degree in Mathematical Engineering: 6 (workload 150 hours)
Bachelor Degree in Mathematics: 6 (workload 150 hours)

Teachers:

Massimiliano Giuli (massimilianodotgiuliatunivaqdotit)

1. Course Objectives

I present and organize the analytical foundations underlying modern economics and finance.

2. Course Contents and learning outcomes (Dublin Descriptors)

Topics of the course include:

  • Sperner’s lemma
  • The Knaster-Kuratowski-Mazurkiewicz lemma
  • Brouwer's fixed point theorem
  • Variational inequalities and equilibrium problems
  • Generalized monotonicity and convexity
  • Brézis-Nirenberg-Stampacchia theorem and Fan's minimax principle
  • Continuity of correspondences
  • Browder, Kakutani and Fan-Glicksberg fixed point theorems
  • Gale-Nikaido-Debreu theorem
  • Nash equilibrium of games and abstract economies
  • Walrasian equilibrium of an economy
  • An application to traffic network

On successful completion of this course, the student should

  • Know the fundamental fixed point theorems for set-valued maps and the basic existence results for equilibrium problems and variational inequalities.
  • Explain some interconnections among these various results.
  • Apply this analysis to game and economic theory

3. Course Prerequisites

I assume familiarity with vector and topological spaces, and with the standard model of the real numbers. I assume that you know the basic facts about metric spaces, normed and seminormerd spaces, Banach and Hilbert spaces.

4. Teaching methods and language

Language:English[info]

5. Assessment Methods

Written and oral

Course information last updated on: 19 gennaio 2018, 17:31